Section 2.2 The Addition Property of Equality 101 �� ������������������������ The Addition Property of Equality ▶ OBJECTIVES As a result of completing this section, you will be able to 1. Define and recognize a linear equation. 2. Use the addition property of equality to solve a linear equation. 3. Solve equations that require more than one step. 4. Solve applications of linear equations. 5. Troubleshoot common errors. The selling price of a new car is $24,891. The selling price is the base price plus fees and options. The base price is $22,985. What is the total of the fees and options? In this section, we use the skills from Section 2.1 to write an equation that represents the situation and to solve the equation using the addition property of equality. Linear Equations In Section 2.1, we defined a mathematical equation. In the remaining sections of this chapter, we focus on one type of equation, a linear equation. ������������������������ A linear equation in one variable is an equation that can be written in the form ax + b = c, where a, b, and c are real numbers and a ≠ 0. The main characteristic of a linear equation in one variable is that the largest exponent of the variable is one. Recall that x = x1. The exponent of one is called the degree of the equation. Linear equations are also called first-degree equations. As we will learn in later chapters, the degree denotes the maximum number of solutions of an equation. Therefore, a linear equation will have one solution except for two special cases, which we will solve in Section 2.4. Some examples of linear equations in one variable are x + 3=-5 2x - 5 = 4x + 1 3(x + 4) = 8 The last two of these linear equations are not in the form ax + b = c. However, we will learn methods that enable us to write these equations in this form. Examples of equations that are not linear are The largest exponent of the variable is 2, not 1. The largest exponent of the variable is 3, not 1. x2 + 5x - 6 = 0 x3 = 8 ���������������������� Recognizing a Linear Equation Step 1: Identify the largest exponent on the variable. Step 2: a. If this exponent is one, then the equation is a linear equation. b. If this exponent is not one, then the equation is not linear. �� ������������������������ ������������������ Determine if the equation is a linear equation in one variable. Problems Solutions 1a. x = 5 The equation x1 = 5 is a linear equation since the largest exponent of the variable is 1. 1b. 2 5 - x = 3 4 (x + 2) The equation 2 5 - x1 = 3 4 (x1 + 2) is a linear equation since both occurrences of the variable x have an exponent of 1. 1c. 3y2 - 4y = 1 The equation 3y2 - 4y = 1 is not a linear equation because the largest exponent of the variable y is 2. Objective 1 ▶ Define and recognize a linear equation.
hendricks_beginning_algebra_1e_ch1_3
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